few_shots: Example:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Mathematical concept/skill options: 
A. Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)
B. Understand place value.
C. Understand the place value system.
D. Extend the counting sequence.
E. Work with numbers 11–19 to gain foundations for place value.
F. Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
G. Perform operations with multi-digit whole numbers and with decimals to hundredths.
H. Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
I. Use place value understanding and properties of operations to add and subtract.


Thought: This set of problems asks students to perform multiplication, which is an operation, on multi-digit whole numbers.
Answer: G

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_000674

5
options: Compute fluently with multi-digit numbers and find common factors and multiples.

Extend the properties of exponents to rational exponents.

Perform arithmetic operations with complex numbers.

Represent and model with vector quantities.

Use complex numbers in polynomial identities and equations.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Know that there are numbers that are not rational, and approximate them by rational numbers.

Use properties of rational and irrational numbers.

Reason quantitatively and use units to solve problems.

Perform operations on vectors.

Perform operations on matrices and use matrices in applications.

Apply and extend previous understandings of numbers to the system of rational numbers.

Represent complex numbers and their operations on the complex plane.

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
problem_activity: Activity
In this activity students continue to build fluency operating with signed numbers as they match different expressions that have the same value. Students look for and use the relationship between inverse operations (MP7).
As students work, identify groups that make connections between the operations, for example they notice that subtracting a number is the same as adding its opposite, or that dividing is the same as multiplying by the multiplicative inverse.
Launch
Arrange students in groups of 2. Distribute pre-cut slips from the blackline master.
Student Facing
Your teacher will give you a set of cards. Group them into pairs of expressions that have the same value.
Student Response
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Anticipated Misconceptions
If students struggle to find matches, encourage them to think of the operations in different ways. You might ask:
How else can you think of ____ (subtraction, addition, multiplication, division)?
Activity Synthesis
Select students to share their strategies. Highlight stategies that compared the structure of the expressions instead of just the final answers.
Discuss:
Subtracting a number is equivalent to adding the additive inverse.
A number and its additive inverse have oppostie signs (but the same magnitude).
Dividing by a number is equivalent to multiplying by the multiplicative inverse.
A number and its multiplicative inverse have the same sign (but different magnitudes).
If desired, have students order their pairs of equivalent expressions from least to greatest to review ordering rational numbers.
Engagement: Develop Effort and Persistence.
Break the class into small discussion groups and then invite a representative from each group to report back to the whole class.
Supports accessibility for: Attention; Social-emotional skills
Speaking, Representing: MLR7 Compare and Connect.
Use this routine to support whole-class discussion. Ask students to consider what is the same and what is different about the structure of each expression. Draw students’ attention to the association between quantities (e.g., adding the additive inverse is subtracting; multiplying by the multiplicative inverse is dividing). These exchanges strengthen students’ mathematical language use and reasoning to describe when comparing inverse-operation relationships involving rational numbers.
Design Principle(s): Support sense-making; Maximize meta-awareness


correct_option_index: 13